Manufacturing process control based on multi-modality and multi-resolution time series data

ABSTRACT

Embodiments describing an approach to aligning multiple time series, calculating an indicator function, estimating a coefficient vector based on the indicator function, and updating the coefficient vector. Additionally, embodiments comprise determining if a change in the coefficient vector is less than a predetermined value, and responsive to determining the change in the coefficient vector is less than the predetermined value outputting a target time series for controlling aluminum smelting.

BACKGROUND OF THE INVENTION

The present invention relates generally to the field of optimizingmanufacturing processes, and more particularly to optimizing aluminumsmelting manufacturing based on multi-modality and multi-resolution timeseries data.

Many complex real applications (e.g., advanced manufacturing processcontrol) involve the collection and modeling of time series data withmulti-modality and multi-resolution. A model is built using such data topredict a target time series which is used for process control, qualityor yield control of the process outputs. Multi-modality is collectedfrom various resources or types of sensors and reflect various controlsignals and their responses. For example, Semiconductor manufacturing,which comprises electrical control signal and responses (resistance,voltage, current), pressure control signal and responses (pressure,valve position), and/or temperature control signal. In another example,Aluminum smelting process, which comprises power related control signaland responses, alumina feed related, noise control related, and/orchemical combination related. Multi-resolution can be a time series dataobtained with different time resolutions. For example, every 10 seconds,every 5 minutes, and/or every 24 hours.

Current practice comprises: aggregating the high-resolution time seriesto obtain low-resolution (e.g., aggregating to the same resolution),calculating summary statistics (e.g., mean, median, std, etc.), and/orinterpolation (e.g., linear, polynomial, etc.). Limitations to thecurrent practice comprise: the potential risk of smoothing out importantsignals available only in the high-resolution, and/or bring errorsbetween time series with large resolution difference by imposingassumptions (e.g., interpolate data collected every 24 hours to every 10seconds). Additionally, currently there is a challenge to integrate theinformation from different modalities and resolutions into a unifiedmodel.

SUMMARY

Embodiments of the present invention disclose a method, a computerprogram product, and a system for optimizing aluminum smelting control,the method comprising: aligning, by one or more processors, multipletime series. Calculating, by the one or more processors, an indicatorfunction. Estimating, by the one or more processors, a coefficientvector based on the indicator function. Updating, by the one or moreprocessors, the coefficient vector. Determining, by the one or moreprocessors, if a change in the coefficient vector is less than apredetermined value, and responsive to determining the change in thecoefficient vector is less than the predetermined value, outputting, bythe one or more processors, a target time series for controllingaluminum smelting.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a functional block diagram illustrating a distributed dataprocessing environment, in accordance with an embodiment of the presentinvention;

FIG. 2A-2B 2A: presents the improved prediction performance in terms ofRoot Mean Square Error (RMSE) using multi-modality multi-resolutionmodel compared to existing model for multi-modality regression (MVRCCA)and modeling based on single resolution data (High Resolution, MedResolution, and Low Resolution); 2B: the prediction model's performanceis robust to the regularization parameter gamma (γ) as the RMSE does notchange much given perturbation of gamma in a small range, i.e. 0 to0.10.

FIG. 3 illustrates operational steps of calibration component, on aclient device within the distributed data processing environment of FIG.1, in accordance with an embodiment of the present invention; and

FIG. 4 depicts a block diagram of components of the server computerexecuting the calibration component within the distributed dataprocessing environment of FIG. 1, in accordance with an embodiment ofthe present invention.

DETAILED DESCRIPTION

Embodiments of the present invention enable an integrated approach tojointly model multi-modality and multi-resolution time series forpredicting target control variables used in advanced manufacturingprocess. Additionally, Embodiments of the present invention enable, anintegrated approach to jointly model the multi-modality andmulti-resolution properties, an optimization approach to reflect boththe quality of fit, and a novel regularizer imposing the consistencyacross multiple modalities and multiple resolutions, and/or an iterationalgorithm to balance between computational complexity and iterationcomplexity for large scale application.

Furthermore, embodiments of the present invention propose advantages andimprovements to the field of manufacturing by effectively leveraginginformation from different modalities compared to simple multiplication,and/or concatenation; effectively leveraging information from differentresolutions compared to aggregate to low and same resolution or summarystatistics; encouraging prediction consistency across both modalitiesand resolutions; linearly scaling for large scale application; andimproving manufacturing process control in finer granularity, all ofwhich improve the art and field of manufacturing.

Implementation of embodiments of the invention may take a variety offorms, and exemplary implementation details are discussed subsequentlywith reference to the Figures.

The programs described herein are identified based upon the applicationfor which they are implemented in a specific embodiment of theinvention. However, it should be appreciated that any particular programnomenclature herein is used merely for convenience, and thus theinvention should not be limited to use solely in any specificapplication identified and/or implied by such nomenclature.

The present invention may be a system, a method, and/or a computerprogram product. The computer program product may include a computerreadable storage medium (or media) having computer readable programinstructions thereon for causing a processor to carry out aspects of thepresent invention.

The computer readable storage medium can be any tangible device that canretain and store instructions for use by an instruction executiondevice. The computer readable storage medium may be, for example, but isnot limited to, an electronic storage device, a magnetic storage device,an optical storage device, an electromagnetic storage device, asemiconductor storage device, or any suitable combination of theforegoing. A non-exhaustive list of more specific examples of thecomputer readable storage medium includes the following: a portablecomputer diskette, a hard disk, a random access memory (RAM), aread-only memory (ROM), an erasable programmable read-only memory (EPROMor Flash memory), a static random access memory (SRAM), a portablecompact disc read-only memory (CD-ROM), a digital versatile disk (DVD),a memory stick, a floppy disk, a mechanically encoded device such aspunch-cards or raised structures in a groove having instructionsrecorded thereon, and any suitable combination of the foregoing. Acomputer readable storage medium, as used herein, is not to be construedas being transitory signals per se, such as radio waves or other freelypropagating electromagnetic waves, electromagnetic waves propagatingthrough a waveguide or other transmission media (e.g., light pulsespassing through a fiber-optic cable), or electrical signals transmittedthrough a wire.

Computer readable program instructions described herein can bedownloaded to respective computing/processing devices from a computerreadable storage medium or to an external computer or external storagedevice via a network, for example, the Internet, a local area network, awide area network and/or a wireless network. The network may comprisecopper transmission cables, optical transmission fibers, wirelesstransmission, routers, firewalls, switches, gateway computers and/oredge servers. A network adapter card or network interface in eachcomputing/processing device receives computer readable programinstructions from the network and forwards the computer readable programinstructions for storage in a computer readable storage medium withinthe respective computing/processing device.

Computer readable program instructions for carrying out operations ofthe present invention may be assembler instructions,instruction-set-architecture (ISA) instructions, machine instructions,machine dependent instructions, microcode, firmware instructions,state-setting data, or source code or object code written in anycombination of one or more programming languages, including an objectoriented programming language such as Smalltalk, C++ or the like, andconventional procedural programming languages, such as the “C”programming language or similar programming languages. The computerreadable program instructions may execute entirely on the user'scomputer, partly on the user's computer, as a stand-alone softwarepackage, partly on the user's computer and partly on a remote computeror entirely on the remote computer or server. In the latter scenario,the remote computer may be connected to the user's computer through anytype of network, including a local area network (LAN) or a wide areanetwork (WAN), or the connection may be made to an external computer(for example, through the Internet using an Internet Service Provider).In some embodiments, electronic circuitry including, for example,programmable logic circuitry, field-programmable gate arrays (FPGA), orprogrammable logic arrays (PLA) may execute the computer readableprogram instructions by utilizing state information of the computerreadable program instructions to personalize the electronic circuitry,in order to perform aspects of the present invention.

Aspects of the present invention are described herein with reference toflowchart illustrations and/or block diagrams of methods, apparatus(systems), and computer program products according to embodiments of theinvention. It can be understood that each block of the flowchartillustrations and/or block diagrams, and combinations of blocks in theflowchart illustrations and/or block diagrams, can be implemented bycomputer readable program instructions.

These computer readable program instructions may be provided to aprocessor of a general purpose computer, a special purpose computer, orother programmable data processing apparatus to produce a machine, suchthat the instructions, which execute via the processor of the computeror other programmable data processing apparatus, create means forimplementing the functions/acts specified in the flowchart and/or blockdiagram block or blocks. These computer readable program instructionsmay also be stored in a computer readable storage medium that can directa computer, a programmable data processing apparatus, and/or otherdevices to function in a particular manner, such that the computerreadable storage medium having instructions stored therein comprises anarticle of manufacture including instructions which implement aspects ofthe function/act specified in the flowchart and/or block diagram blockor blocks.

The computer readable program instructions may also be loaded onto acomputer, other programmable data processing apparatus, or other deviceto cause a series of operational steps to be performed on the computer,other programmable apparatus or other device to produce a computerimplemented process, such that the instructions which execute on thecomputer, other programmable apparatus, or other device implement thefunctions/acts specified in the flowchart and/or block diagram block orblocks.

The flowchart and block diagrams in the Figures illustrate thearchitecture, functionality, and operation of possible implementationsof systems, methods, and computer program products according to variousembodiments of the present invention. In this regard, each block in theflowchart or block diagrams may represent a module, a segment, or aportion of instructions, which comprises one or more executableinstructions for implementing the specified logical function(s). In somealternative implementations, the functions noted in the blocks may occurout of the order noted in the Figures. For example, two blocks shown insuccession may, in fact, be executed substantially concurrently, or theblocks may sometimes be executed in the reverse order, depending uponthe functionality involved. It can also be noted that each block of theblock diagrams and/or flowchart illustration, and combinations of blocksin the block diagrams and/or flowchart illustration, can be implementedby special purpose hardware-based systems that perform the specifiedfunctions or acts or carry out combinations of special purpose hardwareand computer instructions.

The descriptions of the various embodiments of the present inventionhave been presented for purposes of illustration, but are not intendedto be exhaustive or limited to the embodiments disclosed. Manymodifications and variations can be apparent to those of ordinary skillin the art without departing from the scope and spirit of the invention.The terminology used herein was chosen to best explain the principles ofthe embodiment, the practical application or technical improvement overtechnologies found in the marketplace, or to enable others of ordinaryskill in the art to understand the embodiments disclosed herein.

FIG. 1 is a functional block diagram illustrating a distributed dataprocessing environment, generally designated 100, in accordance with oneembodiment of the present invention. The term “distributed” as used inthis specification describes a computer system that includes multiple,physically distinct devices that operate together as a single computersystem. FIG. 1 provides only an illustration of one implementation anddoes not imply any limitations with regard to the environments in whichdifferent embodiments may be implemented. Many modifications to thedepicted environment may be made by those skilled in the art withoutdeparting from the scope of the invention as recited by the claims.

Distributed data processing environment 100 includes mobile device 110,server computer 124, and/or network 130. Network 130 can be, forexample, a telecommunications network, a local area network (LAN), awide area network (WAN), such as the Internet, or a combination of thethree, and can include wired, wireless, or fiber optic connections.Network 130 can include one or more wired and/or wireless networks thatare capable of receiving and transmitting data, voice, and/or videosignals, including multimedia signals that include voice, data, andvideo information. In general, network 130 can be any combination ofconnections and protocols that will support communications betweencomputing device 110 and server computer 120, and other computingdevices (not shown in FIG. 1) within distributed data processingenvironment 100.

In various embodiments, computing device 110 can be, but is not limitedto, a standalone device, a server, a laptop computer, a tablet computer,a netbook computer, a personal computer (PC), a smart phone, a desktopcomputer, a smart television, a smart watch, any programmable electroniccomputing device capable of communicating with various components anddevices within distributed data processing environment 100, via network102 or any combination therein. In general, computing device 110 arerepresentative of any programmable mobile device or a combination ofprogrammable mobile devices capable of executing machine-readableprogram instructions and communicating with users of other mobiledevices via network 130 and/or capable of executing machine-readableprogram instructions and communicating with server computer 120. Inother embodiments, computing device 110 can represent any programmableelectronic computing device or combination of programmable electroniccomputing devices capable of executing machine readable programinstructions, manipulating executable machine readable instructions, andcommunicating with server computer 120 and other computing devices (notshown) within distributed data processing environment 100 via a network,such as network 130.

In various embodiments, computing device 110 includes user interface106, local storage 108, control mechanisms 102, and/or 9-box control104. 9-box control 104 is a functional block that issues a series ofcontrol signals based on the range of temperature and Alumina Fluoride,(i.e., Low (L), Medium (M), and High(H)) concentration. ControlMechanism 102 is a functional block that can issue variable controlsignals. In various embodiments, not depicted in FIG. 1, controlmechanism 102 comprises power control (e.g., voltage, current, etc.),noise control (e.g., change of resistance, heat, etc.), feed control(e.g., feed the alumina dirt), and/or chemical control (e.g., sodium,silicone, iron, and/or other various alloy's known in the art)subcomponents. Computing device 110 and user interface 106 enable a userto interact with smelting optimization component 122 in various ways,such as sending program instructions, receiving program instructions,data entry, displaying data and/or information, editing data, correctingdata, and/or adjusting settings.

User interface (UI) 106 provides an interface to smelting optimizationcomponent 122 on server computer 120 for a user of computing device 110.In one embodiment, UI 106 can be a graphical user interface (GUI) or aweb user interface (WUI) and can display text, documents, web browserwindows, user options, application interfaces, and instructions foroperation, and include the information (such as graphic, text, andsound) that a program presents to a user and the control sequences theuser employs to control the program. In another embodiment, UI 106 canalso be mobile application software that provides an interface between auser of computing device 110 and server computer 120. Mobile applicationsoftware, or an “app,” is a computer program designed to run on smartphones, tablet computers and other mobile devices. In an embodiment, UI106 enables the user of computing device 110 to send, input, edit,correct, update, receive, and/or display data and/or information (e.g.,smelting instructions).

Server computer 120 can be a standalone computing device, a managementserver, a web server, a mobile computing device, or any other electronicdevice or computing system capable of receiving, sending, and processingdata. In other embodiments, server computer 120 can represent a servercomputing system utilizing multiple computers as a server system, suchas in a cloud computing environment. In another embodiment, servercomputer 120 can be a laptop computer, a tablet computer, a netbookcomputer, a personal computer (PC), a desktop computer, a personaldigital assistant (PDA), a smart phone, or any other programmableelectronic device capable of communicating with computing device 110 andother computing devices (not shown) within distributed data processingenvironment 100 via network 130. In another embodiment, server computer120 represents a computing system utilizing clustered computers andcomponents (e.g., database server computers, application servercomputers, etc.) that act as a single pool of seamless resources whenaccessed within distributed data processing environment 100. Servercomputer 120 can include smelting optimization component 122 and sharedstorage 124. Server computer 120 can include internal and externalhardware components, as depicted, and described in further detail withrespect to FIG. 4.

Shared storage 124 and local storage 108 can be a data repository and/ora database that can be written to and/or read by one or a combination ofsmelting optimization component 122, server computer 120 and/orcomputing devices 110. In the depicted embodiment, shared storage 124resides on server computer 120. In another embodiment, shared storage124 can reside elsewhere within distributed data processing environment100 provided coverage assessment program 110 has access to sharedstorage 124. A database is an organized collection of data. Sharedstorage 124 and/or local storage 108 can be implemented with any type ofstorage device capable of storing data and configuration files that canbe accessed and utilized by server computer 120, such as a databaseserver, a hard disk drive, or a flash memory. In other embodiments,shared storage 124 and/or local storage can be hard drives, memorycards, computer output to laser disc (cold storage), and/or any form ofdata storage known in the art. In various embodiments, smeltingoptimization component 122 can store and/or retrieve data from sharedstorage 124 and local storage 108. For example, smelting optimizationcomponent 122 will store image annotation information to shared storage124 and access previously stored image annotation information to assistin future image annotation assignments. In various embodiments, smeltingoptimization component 122 can have cognitive capabilities and learnfrom previous files and/or data that smelting optimization component 122has interacted with previously, and/or has stored to local storage 108and/or shared storage 124. For example, retrieving and analyzingpreviously accessed smelting data from a year ago. In variousembodiments, local storage 108 and/or shared storage 124 can storeprocess data, measurement of 9-box control variables and/or predictionof 9-box control variables.

In various embodiments, smelting optimization component 122 is housed onserver computer 120; however, in other embodiments, smeltingoptimization component 122 can be housed on computing device 110, and/ora computing device and/or server computer not depicted in FIG. 1. Invarious embodiments, multiple control and signal response component(MCSRC) 126 and predictive modeler component (PMC) 128 are subcomponentsof smelting optimization component 122. In various embodiments, MCSRC126 can collect different types of process data at various resolutions.For example, power related process variables are collected every 30minutes, noise related process variables, various feeding parameters arecollected every 1 hour, and various chemical contents are collectedevery 45 minutes, etc. In various embodiments, PMC 128 can use a trainedmodel and iterative algorithm, and takes multi-modality andmulti-resolution time series, to predict control variables. For example,temperature and regulation of Alumina Fluoride, the model in thisparticular example, is trained based on historical process data andhistorical measurements of temperature and Alumina Fluoride. In a moredetailed example, recalling that the optimal Alumina Smeltingtemperature is 1010 degrees Celsius (° C.) and the optimal time sequencefor measuring temperature is every 30 minutes, and maintaining the 1010°C. Alumina Smelting temperature by monitoring the Alumina Smeltingtemperature every 30 minutes and adding/feeding a predetermined amountof Alumina Fluoride to the Alumina Smelting process in order to maintaina consistent temperature of 1010° C.

In one example, challenges of current control practice occur duringmanufacturing processes utilizing aluminum fluoride. In this particularexample, temperature and aluminum fluoride are measured manually andconsume operational resources due to corrosive nature of the plant. Themeasurements are collected in large time intervals, (e.g., every 50-100hours), since it requires long laboratory analysis. However, thepredicted temperature and aluminum fluoride can prompt 9-box control ina finer granularity, proactively response to the abnormal processconditions, improve productivity by reducing energy consumption, andreduce process variation and abnormal events, such as electricalshorting and reoxidation of aluminum.

In various embodiments, predictive modeler 128, depicted in equation 1,can impose the view consistency and resolution coherence in theregularizer R(⋅) by comparing the prediction results with themodality/resolution combinations. This is equivalent to comparing theprediction results with the modality/resolution combination with theaverage over one or more combinations. For example, data from an aluminasmelting process comprises 174 process variables, which are collectedeither every 30 minutes, 2 hours, or 24 hours and includes 4 modalitiescomprising power, noise, feed, and chemical (e.g., MCSRC 126). In thisparticular example, to predict the temperature for process control, PMC128 compares the prediction results with the modality/resolutioncombinations, and the multi-view regression based on canonicalcorrelation analysis (MVRCCA), in which PMC 128 can individually learnfrom one or more resolutions.

Furthermore, in this particular example, PMC 128 conducts a comparisonbased on root mean squared error (RMSE), in which the proposedrand-multi-modality multi-resolution (M3R) method enables an enhancedperformance, rather than the cognitive learning from one or moreresolution individually and the multi-view regression; additionally,rand-M3R is robust to small perturbations in regularization parameter,as seen in FIG. 2A and FIG. 2B. FIG. 2A and FIG. 2B, generallydesignated 200, provides only one example of one implementation and doesnot imply any limitations with regard to environment in which differentembodiments may be implemented. FIG. 2A illustrates the improvedprediction performance in terms of Root Mean Square Error (RMSE) usingmulti-modality multi-resolution model compared to existing model formulti-modality regression (MVRCCA) and modeling based on singleresolution data (High Resolution, Med Resolution, and Low Resolution).FIG. 2B depicts the prediction model's performance to be robust to theregularization parameter gamma (γ) as the RMSE does not change muchgiven perturbation of gamma in a small range, i.e. 0 to 0.10. Let x₁, .. . , x_(N) denote N input process variables (i.e., time series, and t₁,. . . , t_(N) denote the elapsed time between adjacent measurement foreach time series. Traditional techniques for modeling temporal dataassume t_(n)=t, i.e., the data is sampled at the same time stamps forall time series. However, for many real applications, this may not bethe case. For example, in aluminum smelting processes, certain variables(electrical noise related variables) may be sampled with a higherfrequency (e.g., every 10 seconds), and others (e.g. temperature) may besampled with a much lower frequency (e.g., every day). We refer thisproperty as the ‘multi-resolution’ property. Suppose that t₁, . . . ,t_(N) have a set of L unique values.

${\min\limits_{\beta_{1}^{(1)},\ldots \mspace{14mu},\beta_{N}^{(L)}}{\sum\limits_{t}\left( {{y(t)} - {\frac{1}{\sum\limits_{n = 1}^{N}{\sum\limits_{l = 1}^{L}_{n}^{(l)}}} \cdot {\sum\limits_{l = 1}^{L}{\sum\limits_{n = 1}^{N}{_{n}^{(l)}{\sum\limits_{i = 1}^{I^{(l)}}{\beta_{n,i}^{(l)}{x_{n\;}^{(l)}\left( {t - {i \times t^{(l)}}} \right)}}}}}}}} \right)^{2}}} + {R\left( {\beta_{1}^{(1)},\ldots \mspace{14mu},\beta_{N}^{(L)}} \right)}$

Equation 1 depicts the predictive modeling approached used by predictivemodeler 128, where ŷ (t) is defined as

${\frac{1}{\sum\limits_{n = 1}^{N}{\sum\limits_{t = 1}^{L}{II}_{n}^{(l)}}} \cdot {\sum\limits_{l = 1}^{L}{\sum\limits_{n = 1}^{N}{\sum\limits_{i = 1}^{I}{\beta_{n,i}^{(l)}{x_{n}^{(l)}\left( {t - {i \times t^{(l)}}} \right)}}}}}},$

and y>0 is a weight parameter.

I^((l)) is the lag for the l^(th) resolution, and R(⋅) is the proposedregularizer that depends on both the input time series as well as thecoefficient vectors defined as follows:

${R\left( {\beta_{1}^{(1)},\ldots \mspace{14mu},\beta_{N}^{(L)}} \right)} = {\gamma {\sum\limits_{l,n}{_{n}^{(l)}{\sum\limits_{t}\left( {{\sum\limits_{i = 1}^{I^{(l)}}{\beta_{n,i}^{(l)}{x_{n}^{(l)}\left( {t - {i \times t^{(l)}}} \right)}}} - {\hat{y}(t)}} \right)^{2}}}}}$

The objective function consists of two parts. The first part measuresthe goodness of fit. For each time stamp t, the target output y(t) isestimated by computing the average over at least one of the time seriesand at least one of the available resolutions. And the second partconsists of the regularizer R(⋅), which is designed in such a way thatmeasures both view consistency and resolution coherence. To be specific,it ensures that the prediction results from different modalities anddifferent resolutions should be similar to each other. Notice that it issignificantly different from existing multi-view regularizers in thesense that the different modalities area allowed to have differentresolutions, whereas existing regularizers assume (explicitly orimplicitly) that all the modalities have the same resolution.

FIG. 3 is a flowchart depicting operational steps of smeltingoptimization component 122, generally designated 300, on server computer120 within distributed data processing environment 100 of FIG. 1, inaccordance with an embodiment of the present invention. It should beappreciated that FIG. 3 provides only an illustration of oneimplementation and does not imply any limitations with regard to theenvironments in which different embodiments can be implemented. Manymodifications to the depicted environment can be made.

In step 302, smelting optimization component 122 aligns multiple timeseries. In other embodiments, smelting optimization component 122 canalign one or more time series. In various embodiments, smeltingoptimization component 122 aligns one or more time series based onadjacent time stamp of the lowest resolution. In various embodiments,smelting optimization component 122 can directly learn from the originaltime series instead of aggregated data to avoid eliminating data thatonly exists in high resolution. Additionally, in various embodiments,smelting optimization component 122 does not interpolate among differentresolutions to avoid imposing wrong assumption. For example, linearinterpolation between data collected every 24 hours and 10 seconds.

In step 304, PMC 128 calculates the lag between input time series andtarget time series (y(t), e.g. temperature or aluminum fluoride). Invarious embodiments, PMC 128 and/or smelting optimization component 122can calculate the lag between input time series and target time series,in which PMC 128 and/or smelting optimization component 122 can directlyleveraging cross correlation between target time series and one or moreinput time series at the original resolutions, which reflects truerelationship between the input and target time series.

In step 306, PMC 128 initializes the coefficient vector (β_(n,i) ^(l))for the modality, the resolution, and/or time stamp. In variousembodiments, PMC 128 and/or smelting optimization component 122 caninitialize the coefficient vector for the modality, the resolution,and/or time stamp to a set integer. For example, initializing thecoefficient vector for the modality, the resolution, and time stamp tozero.

In step 308, PMC 128 calculates the indicator function. In variousembodiments, PMC 128 can set the corresponding indicator function

_(n) ^((l)) as 1 when the n^(th) modality on the l^(th) resolution isavailable. In various embodiments, PMC 128 and/or smelting optimizationcomponent 122 can calculate one or more indicator functions based ondata availability at modality and resolution. In various embodiments,PMC 128 and/or smelting optimization component can jointly learn fromone or more modalities and resolutions to improve prediction accuracy.

In step 310, PMC 128 estimates the coefficient vector. In variousembodiments, PMC 128 and/or smelting optimization component 122 canestimate the coefficient vector and minimize the difference betweentarget time series and the prediction. Additionally, in variousembodiments, PMC 128 and/or smelting optimization component 122 canestimate the coefficient vector for one or more resolution, modality,and/or lag by minimizing the difference between the target time seriesand the average of available modalities, resolutions, and/or lags overone or more time stamps.

In step 312, PMC 128 computes the average. In various embodiments, PMC128 and/or smelting optimization component 122 can compute the average(y(t)) over one or more modalities, and/or one or more resolutions, forone or more stamp t.

In step 314, PMC 128 can update the coefficient vector. In variousembodiments, PMC 128 and/or MCSR 126 can update the coefficient vectorfor one or more resolution, modality, and/or lag by minimizing thedifference between the prediction results and the average. Additionally,in various embodiments, PMC 128 and/or MCSR 126 can impose predictionconsistence among multiple (e.g., one or more) modalities and enhancecoherence between resolutions to improve prediction accuracy.

In step 316, PMC 128 determines if the change in coefficient vectors isless than a predetermined value. In various embodiments, PMC 128 and/orsmelting optimization component 122 can determine if the change incoefficient vectors is less than a predetermined value, in which PMC 128and/or smelting optimization component 122 are responsive to the changein coefficient vectors. In this particular example, if the change incoefficient vectors is higher than the predetermined value (No branch)PMC 128 can repeat steps 310 through 316; however, if PMC 128 determinesthe change of coefficient vectors is less than the predetermined value(Yes branch), PM will advance to step 318.

In step 318, MCSR 126 outputs the target time series. In variousembodiments, MCSR 126 and/or smelting optimization component 122 canoutput one or more target time series and/or provide data to controlmechanism 102 and/or 9-box control. For example, outputting thetemperature of the aluminum smelting process for control andinstructions on how much Alumina Fluoride to feed into the cell (e.g.,pot) for smelting. In various embodiments, MCSR 126 can output thetarget time series to a user as a notification of the updateinformation/data. In various embodiments, MCSR 126 can output the targettime series as a prompt to a user and request a user's response to theoutput notification. In other embodiments, MCSR 126 can output targettime series and act on the information/data automatically.

FIG. 4 depicts a block diagram of components of server computer 104within distributed data processing environment 100 of FIG. 1, inaccordance with an embodiment of the present invention. It should beappreciated that FIG. 4 provides only an illustration of oneimplementation and does not imply any limitations with regard to theenvironments in which different embodiments can be implemented. Manymodifications to the depicted environment can be made.

FIG. 4 depicts a block diagram of components of a computing devicewithin distributed data processing environment 100 of FIG. 1, inaccordance with an embodiment of the present invention. It should beappreciated that FIG. 3 provides only an illustration of oneimplementation and does not imply any limitations with regard to theenvironments in which different embodiments can be implemented. Manymodifications to the depicted environment can be made.

FIG. 4 depicts computer system 400, where server computer 102 representsan example of computer system 400 that includes smelting optimizationcomponent 122. The computer system includes processors 401, cache 403,memory 402, persistent storage 405, communications unit 407,input/output (I/O) interface(s) 406 and communications fabric 404.Communications fabric 404 provides communications between cache 403,memory 402, persistent storage 405, communications unit 407, andinput/output (I/O) interface(s) 406. Communications fabric 404 can beimplemented with any architecture designed for passing data and/orcontrol information between processors (such as microprocessors,communications and network processors, etc.), system memory, peripheraldevices, and any other hardware components within a system. For example,communications fabric 404 can be implemented with one or more buses or acrossbar switch.

Memory 402 and persistent storage 405 are computer readable storagemedia. In this embodiment, memory 402 includes random access memory(RAM). In general, memory 402 can include any suitable volatile ornon-volatile computer readable storage media. Cache 403 is a fast memorythat enhances the performance of processors 401 by holding recentlyaccessed data, and data near recently accessed data, from memory 402.

Program instructions and data used to practice embodiments of thepresent invention may be stored in persistent storage 405 and in memory402 for execution by one or more of the respective processors 401 viacache 403. In an embodiment, persistent storage 405 includes a magnetichard disk drive. Alternatively, or in addition to a magnetic hard diskdrive, persistent storage 405 can include a solid state hard drive, asemiconductor storage device, read-only memory (ROM), erasableprogrammable read-only memory (EPROM), flash memory, or any othercomputer readable storage media that is capable of storing programinstructions or digital information.

The media used by persistent storage 405 may also be removable. Forexample, a removable hard drive may be used for persistent storage 405.Other examples include optical and magnetic disks, thumb drives, andsmart cards that are inserted into a drive for transfer onto anothercomputer readable storage medium that is also part of persistent storage405.

Communications unit 407, in these examples, provides for communicationswith other data processing systems or devices. In these examples,communications unit 407 includes one or more network interface cards.Communications unit 407 may provide communications through the use ofeither or both physical and wireless communications links. Programinstructions and data used to practice embodiments of the presentinvention may be downloaded to persistent storage 405 throughcommunications unit 407.

I/O interface(s) 406 enables for input and output of data with otherdevices that may be connected to each computer system. For example, I/Ointerface 406 may provide a connection to external devices 408 such as akeyboard, keypad, a touch screen, and/or some other suitable inputdevice. External devices 408 can also include portable computer readablestorage media such as, for example, thumb drives, portable optical ormagnetic disks, and memory cards. Software and data used to practiceembodiments of the present invention can be stored on such portablecomputer readable storage media and can be loaded onto persistentstorage 405 via I/O interface(s) 406. I/O interface(s) 406 also connectto display 409.

Display 409 provides a mechanism to display data to a user and may be,for example, a computer monitor.

What is claimed is:
 1. A computer-implemented method for optimizingaluminum smelting control, the method comprising: estimating acoefficient vector based on an indicator function; updating thecoefficient vector; determining if a change in the coefficient vector isless than a predetermined value; and responsive to determining thechange in the coefficient vector is less than the predetermined value,outputting a target time series for controlling aluminum smelting. 2.The computer-implemented method of claim 1 further comprising:calculating a lag between one or more input time series and the targettime series.
 3. The computer-implemented method of claim 2 furthercomprising: initializing coefficient vector for at least one of:modality, resolution, or time stamp.
 4. The computer-implemented methodof claim 3 further comprising: computing an average of at least one ofmodality, resolution, or time stamp.
 5. The computer-implemented methodof claim 1, wherein the aligning of multiple time series furthercomprises: aligning one or more time series based on adjacent time stampof a lowest resolution.
 6. The method of claim 2, wherein thecalculating the lag between the one or more input time series and thetarget time series further comprises, directly leveraging crosscorrelation between the target time series and the one or more inputtime series at one or more predetermined resolutions.
 7. The method ofclaim 1, wherein updating the coefficient vector further comprises,updating the coefficient vector for at least one of a one or moreresolutions, modality, or lag by minimizing a difference between aprediction results and the average.
 8. A computer program product foroptimizing aluminum smelting control, the computer program productcomprising: one or more computer readable storage devices and programinstructions stored on the one or more computer readable storagedevices, the stored program instructions comprising: programinstructions to estimate a coefficient vector based on the indicatorfunction; program instructions to update the coefficient vector; programinstructions to determine if a change in the coefficient vector is lessthan a predetermined value; and responsive to determining the change inthe coefficient vector is less than the predetermined value, programinstructions to output a target time series for controlling aluminumsmelting.
 9. The computer program of claim 8 further comprising: programinstructions to calculate a lag between one or more input time seriesand the target time series.
 10. The computer program of claim 9 furthercomprising: program instructions to initialize coefficient vector for atleast one of modality, resolution, or time stamp.
 11. The computerprogram of claim 10 further comprising: program instructions to computean average of at least one of modality, resolution, or time stamp. 12.The computer program of claim 8, wherein the aligning of multiple timeseries further comprises: aligning one or more time series based onadjacent time stamp of a lowest resolution.
 13. The computer program ofclaim 9, wherein program instructions to calculate the lag between theone or more input time series and the target time series furthercomprises, directly leveraging cross correlation between the target timeseries and the one or more input time series at one or morepredetermined resolutions.
 14. The computer program of claim 8, whereinupdating the coefficient vector further comprises, updating thecoefficient vector for at least one of a one or more resolutions,modality, or lag by minimizing a difference between a prediction resultsand an average.
 15. A computer system for optimizing aluminum smeltingcontrol, the computer system comprising: one or more computerprocessors; one or more computer readable storage devices; programinstructions stored on the one or more computer readable storage devicesfor execution by at least one of the one or more computer processors,the stored program instructions comprising: program instructions toestimate a coefficient vector based on the indicator function; programinstructions to update the coefficient vector; program instructions todetermine if a change in the coefficient vector is less than apredetermined value; and responsive to determining the change in thecoefficient vector is less than the predetermined value, programinstructions to output a target time series for controlling aluminumsmelting.
 16. The computer system of claim 15 further comprising:program instructions to calculate a lag between one or more input timeseries and the target time series.
 17. The computer system of claim 16further comprising: program instructions to initialize coefficientvector for at least one of modality, resolution, or time stamp.
 18. Thecomputer system of claim 17 further comprising: program instructions tocompute an average of at least one of modality, resolution, or timestamp.
 19. The computer system of claim 15, wherein the aligning ofmultiple time series further comprises: aligning one or more time seriesbased on adjacent time stamp of a lowest resolution.
 20. The computersystem of claim 16, wherein program instructions to calculate the lagbetween the one or more input time series and the target time seriesfurther comprises, directly leveraging cross correlation between thetarget time series and the one or more input time series at one or morepredetermined resolutions.